The present invention relates to a method of analyzing an electromagnetic field created in a rotary machine, such as a generator or a motor, and an electromagnetic field analyzer.
A time step method carries out the sequential analysis of an electromagnetic field that induces an eddy current in a rotary machine by turning a rotor little by little. This known time step method is mentioned in H.C. Lai, D. Rodger and P.J. Leonard, xe2x80x9cCoupling meshes in 3D problems involving movementsxe2x80x9d, IEEE Transactions on Magnetics, Vol. 28, No. 2, pp. 1732-1734 (1992).
A technique disclosed in Japanese Patent Laid-open No. Hei 7-198810 divides the results of magnetic field analysis into a plurality of groups, subjects each group to a spatial harmonic analysis and time harmonic analysis, and separates the same into a positive-phase-sequence component and a negative-phase-sequence component.
The time step method where the rotor is turned stepwise for sequential analysis is effective as a transient analyzing method. However, when obtaining a steady state solution, a synchronous rotary machine requires a several turns for rotation analysis and an induction rotary machine requires several tens to several hundreds of turns for rotation analysis before the solution settles down in a steady state. The number of time steps in one turn nearly equals the number of elements arranged along the direction of rotation and is as large as a hundred. Therefore, several hundreds time steps are necessary for the analysis of the a synchronous machine, and several thousands to several tens of thousands of time steps are necessary for the analysis of an induction machine. Therefore, there was a problem that a very large computation time is consumed for obtaining a steady state solution.
Accordingly, it is an object of the present invention to provide a fast analyzing method for electromagnetic fields of rotary machines in a steady or quasi-steady state, and an electromagnetic field analyzer based on the method.
With the foregoing object in view, the present invention is characterized by analyzing an electromagnetic field in a total analysis space of a rotary machine consisting of two partial spaces, i.e., a stator space containing a stator and a rotor space containing a rotor to determine a boundary field between the stator space and the rotor space; expanding the boundary field into modes along a direction of rotation; converting the obtained modes into rotating magnetic field components; and analyzing electromagnetic fields individually in the stator space and the rotor space by using the obtained rotating magnetic field components as boundary conditions on the slip surface of the stator space and the rotor space.
According to the present invention, a steady-state solution or a quasi-steady-state solution of an electromagnetic field in a rotary machine can be acquired by several iterations of calculation. Since the boundary field between the stator space and the rotor space is updated successively taking the influence of an obtained eddy current into consideration, a self-consistent solution can be obtained for the total analysis space by executing the electromagnetic field analyzing method of the present invention several times.
The obtained modes may be converted into rotating magnetic field components after excluding periodically fluctuating components of a magnetic circuit system between the stator and rotor.
The obtained modes may be converted into complex rotating components of the magnetic field after excluding periodically fluctuating components of a magnetic circuit system between the stator and the rotor, and the complex rotating components as a boundary condition may be assigned on the boundary surface between the stator space and the rotor space in a stationary coordinate system for the stator space and in a rotatory coordinate system for the rotor space.
The total space analysis and the partial space analysis may be alternatively repeated where the eddy current obtained in the partial space analysis is regarded as a given current in the total space analysis.
The mode expansion can be applied in the edge finite element method by radially dividing an air gap between the rotor and the stator into three or more layers in a meshing process, and by dividing the air gap into elements so that the edges at the same axial position on the slip surface approximately coincide with each other by rotating around the rotation axis.